Breather trapping and breather transmission in a DNA model with an interface

Abstract

We study the dynamics of moving discrete breathers in an interfaced piecewise DNA molecule. This is a DNA chain in which all the base pairs are identical and there exists an interface such that the base pairs dipole moments at each side are oriented in opposite directions. The Hamiltonian of the Peyrard-Bishop model is augmented with a term that includes the dipole-dipole coupling between base pairs. Numerical simulations show the existence of two dynamical regimes. If the translational kinetic energy of a moving breather launched towards the interface is below a critical value, it is trapped in a region around the interface collecting vibrational energy. For an energy larger than the critical value, the breather is transmitted and continues travelling along the double strand with lower velocity. Reflection phenomena never occur.The same study has been carried out when a single dipole is oriented in opposite direction to the other ones. When moving breathers collide with the single inverted dipole, the same effects appear. These results emphasize the importance of this simple type of local inhomogeneity as it creates a mechanism for the trapping of energy.Finally, the simulations show that, under favorable conditions, several launched moving breathers can be trapped successively at the interface region producing an accumulation of vibrational energy. Moreover, an additional colliding moving breather can produce a saturation of energy and a moving breather with all the accumulated energy is transmitted to the chain.

Nonsymmetric moving breather collisions in the Peyrard-Bishop DNA model

“…To obtain MBs, each breather should be perturbed using the initial conditions given by Eqs. (4). To obtain nonsymmetric collisions each perturbation must be different.…”

“…Some studies about the existence and properties of MBs in the Peyrard-Bishop model including dipole-dipole dispersive interaction are carried out in [11] [4].…”

Mobile breathers in a Nonlinear model for DNA breathing

“…The method used for calculating discrete breathers in (KG) lattices consists on approximating the dynamical equations by a Nonlinear Schrodinger Equation (NLS) and moving the breather by an envelope solution 17 . Cuevas, Palmero, Romero and Archilla have found that the moving breather can cross the impurity, and can be reflected by it, or can be trapped 18,19 . The problem is to determine the parameters of the model to generate a trapped breather (TB) which is very important for the DNA transcription.…”

High-order nonlinear excitations in the Joyeux-Buyukdagli model of DNA

“…In this model, the double strand corresponds to a Klein-Gordon chain, the variable parameters are the distances between nucleotides within each base pair, and only short-range interactions are considered because of the stacking coupling [17]. It is well known that the Peyrard-Bishop (PB) model can produce solitons due to the balanced competition between dispersion and nonlinear effects [18][19][20]. For example, in the continuum limit, nonlinear equations of motion for the system reduce to a pair of sine-Gordon-type equations, which have kink soliton solutions [21].…”